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Simplifying (7 + -4i) + -1(a + bi) = 12 + 5i Remove parenthesis around (7 + -4i) 7 + -4i + -1(a + bi) = 12 + 5i 7 + -4i + (a * -1 + bi * -1) = 12 + 5i 7 + -4i + (-1a + -1bi) = 12 + 5i Reorder the terms: 7 + -1a + -1bi + -4i = 12 + 5i Solving 7 + -1a + -1bi + -4i = 12 + 5i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -1a + -1bi + -7 + -4i = 12 + -7 + 5i Reorder the terms: 7 + -7 + -1a + -1bi + -4i = 12 + -7 + 5i Combine like terms: 7 + -7 = 0 0 + -1a + -1bi + -4i = 12 + -7 + 5i -1a + -1bi + -4i = 12 + -7 + 5i Combine like terms: 12 + -7 = 5 -1a + -1bi + -4i = 5 + 5i Add 'bi' to each side of the equation. -1a + -1bi + bi + -4i = 5 + bi + 5i Combine like terms: -1bi + bi = 0 -1a + 0 + -4i = 5 + bi + 5i -1a + -4i = 5 + bi + 5i Add '4i' to each side of the equation. -1a + -4i + 4i = 5 + bi + 5i + 4i Combine like terms: -4i + 4i = 0 -1a + 0 = 5 + bi + 5i + 4i -1a = 5 + bi + 5i + 4i Combine like terms: 5i + 4i = 9i -1a = 5 + bi + 9i Divide each side by '-1'. a = -5 + -1bi + -9i Simplifying a = -5 + -1bi + -9i
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